Hamiltonian and gradient properties of certain type of dynamical systems

TL;DR

This paper investigates the properties of Hamiltonian and gradient flows in specific dynamical systems, focusing on conditions where Hamiltonian dynamics dominate and analyzing simple Hamiltonian cases for oscillatory behavior.

Contribution

It introduces conditions under which Hamiltonian dynamics are dominant in certain neural network-inspired systems and studies simple Hamiltonian models for oscillation patterns.

Findings

Hamiltonian properties can dominate in specific neural network dynamics.

Simple Hamiltonian models exhibit oscillatory patterns under certain conditions.

Conditions for the dominance of Hamiltonian flow are identified.

Abstract

From the sandpoint of neural network dynamics we consider dynamical system of special type pesesses gradient (symmetric) and Hamiltonian (antisymmetric) flows. The conditions when Hamiltonian flow properties are dominant in the system are considered. A simple Hamiltonian has been studied for establishing oscillatory patern conditions in system under consideration.